Soheyla Feyzbakhsh (Online)
We will first discuss a general criterion that ensures a fractional Calabi-Yau category of dimension less than or equal to 2 admits a unique Serre-invariant stability condition up to the action of the universal cover of GL+(2, R). This result can be applied to a certain triangulated subcategory (called the Kuznetsov component) of the bounded derived category of coherent sheaves on a cubic threefold. As an application, we will prove (i) a categorical version of the Torelli theorem holds for cubic threefolds, and (ii) the moduli space of Ulrich bundles of fixed rank r greater than or equal to 2 on a cubic threefold is irreducible. The talk is based on joint work with Laura Pertusi and a group project with A. Bayer, S.V. Beentjes, G. Hein, D. Martinelli, F. Rezaee and B. Schmidt.